Roller Coaster G-Force Lab (2D)

This 2D companion looks at the same ride from the rider's seat rather than the energy books: every point of the track carries an exact, analytically-built signed curvature κ = ±1/r, so the apparent-weight formula N/m = v²·κ + g·cosθ can be evaluated exactly instead of estimated from a finite-difference slope. Pick one of four track shapes, tighten the hill/valley radius to sharpen the G swings, and change the launch speed and cart mass to watch the live G-meter swing from true airtime (negative G on a sharp crest) to multiple-g compression at the bottom of a deep valley — with the full G-vs-position curve for the current settings drawn analytically before the cart even leaves the platform.